Reputation
14,463
Top tag
Next privilege 15,000 Rep.
Protect questions
Badges
2 32 98
Newest
 Good Answer
Impact
~361k people reached

1d
awarded  Good Answer
1d
awarded  Popular Question
Jun
30
answered What is the 'optimal' equal-area partition of a circle?
Jun
24
awarded  Popular Question
Jun
23
awarded  Nice Answer
Jun
19
awarded  limits
Jun
16
comment Linear algebra: Proving uniqueness and existence of a function
I do not have the time right now to write an answer. Look at the Gramm-Schmidt process. In that process the initial operations are only operations of type 2) , so there is no change in the value of the function. Changes come when you normalize, whcih is an operation of type 3). If you write things down and use 4, you get an explicit formula, which gives unicity.
Jun
16
comment Linear algebra: Proving uniqueness and existence of a function
You're probably on the right track with that function. The hints are valid though. You can prove existence and uniqueness by using the properties given without using the determinant. In fact, this is now one can prove that the function determinant exists without really writing the formula.
Jun
5
comment Proof of $\sum_{x = 1}^\infty \frac{1}{x}$'s divergence by absurdity?
Yes, the proof is valid (as far as I can tell). The only troubling part is the rearrangement of the terms of a series, grouping and splitting, which cannot be done in general. But assuming convergence, you have, in fact, absolute convergence, and the operations you make are valid.
Jun
5
answered Proof of $\sum_{x = 1}^\infty \frac{1}{x}$'s divergence by absurdity?
Jun
1
comment How many 3 digit even numbers can be formed by using digits 1,2,3,4,5,6,7 ,if no digits are repeated
That depends on how you look at things. :)
Jun
1
answered How many 3 digit even numbers can be formed by using digits 1,2,3,4,5,6,7 ,if no digits are repeated
May
27
accepted Simpler proof - Non atomic measures
May
26
awarded  Popular Question
May
17
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
Continuity alone is not sufficient. Continuity plus two different solutions give an infinity of solutions. Think that $f$ Lipschitz (which is continuous) implies unique solution.
May
17
comment Show that $ \int_{-\infty}^{\infty} \frac{x^3}{(x^2+4)(x^2+1)}\, dx$ does not converge
If $a=b$ you integrate an odd function on $[-a,a]$ so you get $0$.
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
I do not get the question regarding the sufficiency. Can you please detail what you mean?
May
16
comment Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
@S.Panja-1729: Wikipedia is only as right as the people contributing to it. So the question "is wikipedia wrong?" can well be answered "Yes" in plenty of situations. You can see in the comments to your questions that the equation you mention has infinitely many solutions.
May
16
answered Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
May
16
revised Is Lipschitz's condition necessary for existence of unique solution of an I.V.P.?
deleted 14 characters in body